Modified Riccati Equation Emanating from Lainiotis Filter

The modified Riccati equation arises in the implementation of Kalman filter in target tracking under measurement uncertainty and it cannot be transformed in an equation of the form of the Riccati equation. The modified Riccati equation emanating from Lainiotis filter is derived. It is shown that the two equations have the same behavior: if the system is stable, then there exists a steady state solution, while if the system is unstable, then there exists a critical value of the measurement detection probability, below which the modified Riccati equations diverge. It is established that this critical value increases in a logarithmic way, as the system becomes more unstable.